Concentrations of cosmogenic iodine, 129I, in the pore fluid of marine sediments often indicate that the pore fluid is much older than the host sediment, even when vertical flow due to sediment compaction is taken into account. Old pore fluid has been used in previous studies to argue for pervasive upward fluid flow and a deep methane source for hydrate deposits. Alternatively, old pore fluid age may reflect more complex flow patterns. We use a two-dimensional numerical transport model to account for the effects of topography and fractures on pore fluid pathlines when sediment permeability is anisotropic. We find that fluid focusing can cause significant lateral migration as well as regions where downward flow reverses direction and returns toward the seafloor. Longer pathlines can produce pore fluid ages much older than that expected with a one-dimensional compaction model. For steady-state models with geometry representative of Blake Ridge (USA), a well-studied hydrate province, we find pore fluid ages beneath regions of topography and within fractured zones that are up to 70 Ma old. Our results suggest that the measurements of 129I/127I reflect a mixture of new and old pore fluid. However, old pore fluid need not originate at great depths. Methane within pore fluids can travel laterally several kilometers, implying an extensive source region around the deposit. This type of focusing should aid hydrate formation beneath topographic highs.
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 Methane hydrate is an icy solid which can sequester large amounts of methane gas within its crystal structure. Methane hydrate typically occurs naturally along many continental margins, where deep water and cold temperatures provide the necessary thermodynamic conditions. Organic-rich sediments preferentially host hydrate by providing a source of methane gas [Kvenvolden, 1998; Sloan & Koh, 2007].
 It is currently thought that methane is transported to the hydrate stability zone by a combination of fluid advection and bubble migration. One-dimensional sediment compaction models predict pore fluid flow which is downward relative to the seafloor (e.g., [Hutchison, 1985]). Such a flow carries dissolved methane downward through the hydrate stability zone. Because the methane solubility increases with depth in the stability zone [Davie et al., 2004; Sun & Duan, 2007], the fluid becomes increasingly undersaturated in methane. This would inhibit formation or lead to dissolution of hydrate (if present) without additional sources of methane (e.g., biogenic production). Conversely, upward flow promotes hydrate formation by supplying methane from below the stability zone. Many hydrate modeling studies have invoked a deep source of upward flowing methane-bearing fluid to explain the observed abundance [Hyndman & Davis, 1992; Xu & Ruppel, 1999; Egeberg & Dickens, 1999; Ruppel & Kinoshita, 2000; Davie & Buffett, 2001; Pecher et al., 2001].
 The origin of the upward flow is not well understood. It is contradictory to the predictions of a one-dimensional compaction model, which implies that more complex flows are necessary. Many complications exist in natural settings, including spatial variations in the lithography, fractures, etc. In a previous publication [Frederick & Buffett, 2011], we have shown that pore fluid focusing in compacting marine sediments is a possible mechanism to create local upward flow when sediments have anisotropic permeability and bedding planes are sloped due to seafloor topography. Fractures can cause similar fluid focusing because of the localized enhancement of vertical sediment permeability.
 The focusing of pore fluids beneath topographic highs or toward fractured zones causes significant lateral migration through the host sediments. As a result, fluid parcels travel substantially longer distances compared with vertical paths expected from a one-dimensional compaction model. The age of the pore fluid increases with the distance travelled after sediment deposition (i.e., when the pore space becomes isolated from seawater).
 In natural settings, pore fluid age can be inferred from measurements of iodine isotope concentrations. 127I is the only stable isotope of iodine, while 129I is a cosmogenic radioisotope, produced either by spontaneous fission of 238U (e.g., in situ production) or cosmic ray spallation of Xe isotopes in the atmosphere. Iodine is isotopically homogenous at the surface of the Earth and within its oceans and is readily incorporated into living tissues at the surface ratio of (129I/127I)0 = 1500 × 10−15, ignoring recent anthropogenic disturbances [Edwards, 1962]. Once the iodine (as part of organic matter) is deposited on the seafloor, its isotopic ratio decreases as 129I decays radioactively. Iodine is released into the pore fluid when the organic matter decomposes and can then begin to migrate via fluid advection or diffusion. By measuring the pore fluid's 129I/ 127I ratio, an estimate of the parent organic material's age is obtained from,
where λ = 4.41e − 8 yr − 1 is the 129I decay constant, and t is time, in years, since deposition at the seafloor. The iodine age can be used as a proxy for the pore fluid age with certain assumptions. If iodine diffusion is small (e.g., iodine travels mainly by fluid advection), organic matter decomposition is limited to very near the seafloor, and in situ iodine production is negligible, the age of the pore fluid should be exactly the age of the parent organic material (e.g., the iodine age). In such cases, the iodine isotope ratio can be treated as a conservative tracer. The assumption of no in situ production can be relaxed if the measured iodine concentration is corrected using estimates of 238U abundance in the sediments. Without correction, in situ iodine production tends to make the pore fluid appear younger.
 Pore fluid ages have been measured at several methane hydrate provinces using 129I/127I ratios [Fehn et al., 2000, 2003, 2006; Tomaru et al., 2007b, 2009, Lu et al., 2008a; Muramatsu et al., 1997]. These studies always find that the pore fluid is much older than the host sediments. Although one-dimensional compaction models indicate that the pore fluid is expected to be older than the host sediments due to fluid expulsion during sediment compaction, the observed age far exceeds this expectation. For example, pore fluid ages measured at Blake Ridge site 997 by Fehn et al.  range between 40 and 70 Ma in the shallow sediments (300–700 mbsf). By comparison, Fehn et al.  expect a pore fluid age between 4 and 10 Ma based on a one-dimensional compaction model.
 The existence of more complicated flow patterns, such as fluid focusing, should be observable (although indirectly) due to its effect on iodine transport, and thus pore fluid age. Pore fluid focusing beneath topographic features or toward fractured regions in the sediments can enhance fluid flow and solute transport from depth. Iodine's strong association with organic matter plausibly connects it to the methane source in marine sediments. Such mechanisms provide a simple explanation for the preferential accumulation of hydrate under topographic highs or within fractures, as has been reported at Blake Ridge [Paull et al., 2000]. The goal of this study is to characterize the influence of fluid focusing on pore fluid age and investigate whether such flows can explain the observations at Blake Ridge.
2 Compaction-driven Fluid Flow
 The decrease in sediment porosity with depth, y, due to steady mechanical compaction is often described empirically by a modified form of Athy's Law [Athy, 1930] as
where ϕ(0) is the sediment porosity at the seafloor, ϕ(∞) is the fully compacted sediment porosity at depth, and L is the characteristic length scale for compaction. We estimate L by fitting ((2)) to observations at Blake Ridge and explore a range of values for ϕ(∞). We chose a reference value of ϕ(∞) = 0.25, which is roughly equal to the minimum void space in a dense arrangement of closely packed spheres [Conway & Sloane, 1998], but note that lower porosity can develop as the solid grains deform [Palciauskas & Domenico, 1989].
 In a reference frame fixed to the seafloor, the one-dimensional solution for sediment vs and fluid vf velocity is
where is the sedimentation rate and D represents the depth where fluid is immobile within the sediments. A positive velocity indicates downward movement relative to the seafloor. We adapt constant values for both and D.
 When fluid is expelled from the sediment pore space into the surroundings due to compaction, the fluid flux qc, or transport velocity, is described by Darcy's Law,
which is valid for laminar flow through a porous media. The gradient in excess (or nonhydrostatic) pore pressure ∇ P∗ due to sediment loading drives the flow of fluid with a viscosity μ.
 Bulk sediment permeability is described by K, which is a tensor when permeability is anisotropic,
Bulk permeability along the bedding layers (Kh) can be several orders of magnitude larger than that across the bedding layers (Kv) [Phillips, 1991]. The presence of fractures can also introduce anisotropy by enhancing the permeability in the direction of fracture. We use K to capture the effects of lithologic layering when the grid spacing is too coarse to resolve individual layers or fractures. The ratio of horizontal to vertical permeability, Kh/Kv, gives the strength of anisotropy. The local angle of the bedding planes is used to rotate the permeability tensor K from the frame of the bedding planes into the frame of the computations. The resulting off-diagonal terms in K couple the horizontal and vertical components of flow.
 Sediment permeability is often approximated as a function of porosity. We use a modified Kozeny-Carman relation [Mavko & Nur, 1997] given by
where K(0) is the permeability of the sediments at the seafloor and ϕc is the percolation porosity. The later represents the fraction of porosity which is disconnected and does not contribute to flow through a porous media.
 The velocity of the pore fluid relative to the seafloor can be found by rearranging Equation ((5)). This gives the expression
The direction of vf depends on the competition between the upward fluid flux relative to the sediment grains, qc, and the downward movement of sediments, vs. In compacting marine sediments, the one-dimensional solution for vf is downward relative to the seafloor. However, pore fluid focusing is one mechanism that can cause qc/ϕ to locally exceed vs, thus creating fluid flow that is locally upward relative to the seafloor. Within sediment layers that are sloped due to topographic features, a preferential flux qc along the bedding layers may bring excess fluid toward topographic highs. Fractured zones act similarly. This fluid flux is drawn laterally from the surroundings and focused into a finite region, potentially increasing the travel path of fluid parcels.
3 Numerical Model
 We apply a previously developed numerical model for the excess pore pressure distribution, P*, within compacting marine sediments (see Frederick & Buffett ). The solution for P* is then used to calculate qc from ((5)), and the pore fluid velocity relative to the seafloor is obtained from the expression vf = qc/ϕ + vs. Pore fluid pathlines are calculated from vf to visualize the flow field. Because the velocity field is steady, these pathlines are identical to streamlines.
 The age of the pore fluid is calculated using a ray tracing method that utilizes fluid pathlines to track 29I and 127I transport throughout the sediments. The concentration of each iodine isotope, CI, is governed by a two-dimensional advection-diffusion equation,
where t is the portion of time that iodine travels with the pore fluid at velocity u, and QI is an iodine source. The effective diffusivity, , depends on the molecular diffusivity in seawater, , and the sediment tortuosity, τ, according to [Berner, 1980],
The value for τ is difficult to measure directly, but can be estimated using Archie's Law [Archie, 1942]. The formation resistivity factor, F = Rs/Rf, gives the ratio of the electrical resistivity of the bulk saturated sediments, Rs, to the electrical resistivity of the pore fluid, Rf, in absence of surface conductivity effects. Because sediment geometry creates a resistance to electrical flow through the bulk relative to the pore fluid, the formation factor can give an estimate of sediment tortuosity, assuming the solid is non-conducting relative to the fluid. Following Ullman & Aller , we relate the tortuosity to the porosity by
Because electrical conductance is analogous to mass diffusion, this relationship can be applied to obtain the effective diffusion coefficient for iodine within marine sediments, giving
The exponent n is obtained empirically, and depends on the depositional environment. A typical value for marine sediments is n = 3 [Archer et al., 1989]. We adapt a constant molecular diffusivity for iodine in seawater ( = 2.05 × 10−9 m2 s−1 at 25 °C [Linde, 2004–2005]). Similarly, we use the average porosity (ϕavg = 0.5) in Equation ((12)) so that is constant throughout the domain. While these parameters provide a reasonable value for , they likely represent an upper bound. Values as large as n = 5.4 have been reported for clay sediments by Atkins & Smith , and the possibility of solute adsorption to clay surfaces during transport [Li & Gregory, 1974] both act to substantially reduce . Because the typical fluid velocities and grain size distributions are small, we can neglect mechanical dispersion effects when scaled against molecular diffusion.
 The two-dimensional solution to Equation ((9)) for the concentration of each iodine isotope is approximated in a Lagrangian frame of reference that follows the fluid parcels. We approximate the solution to Equation ((9)) by solving for the advective and diffusive components separately. First, fluid pathlines are obtained from the velocity field ((8)), and then discretized into a finite number of segments. Next, the average fluid velocity is calculated along each pathline segment. A fluid parcel's travel time along any finite segment is obtained by dividing the segment length by the average fluid velocity along that segment. Finally, summing the travel time along each segment of a pathline gives the accumulated time, tf, required to reach a given point (X, Y) along the pathline, as defined by,
where u = (u,v) is evaluated along the pathline, and the coordinate (xf, yf) denotes the initial position of the fluid parcel when iodine is released into the pore fluid at time tf = 0. Thus, the coordinates (xf, yf) define the start of each pathline.Diffusion causes iodine to spread as the fluid parcel travels along the pathline. A general solution to the diffusion equation for the concentration of iodine is
when the mass of iodine, MI (with units of kg m−1), is initially concentrated in a small volume. In detail, we expect MI to be evenly distributed across a grid cell once iodine is released from the organic matter in the sediments. A more representative initial condition is obtained by evaluating CI (xf, yf,t) at t = Δt, where Δt = Δx2/ is the time required for a concentrated source of iodine to diffuse across a grid cell of dimension Δx. Consequentially, the solution for 127I composition for a single fluid parcel at later times is given by
The concentration for 129I obeys the same equation, but the initial mass decreases with time since deposition due to radioactive decay,
The initial value of is set arbitrarily to 1 kg m−1. An appropriate mass of 129I is also released, whose amount depends on the release location. In natural settings, iodine release depth is a function of organic matter decomposition. However, because rate of decomposition is currently uncertain, we adapt two end-member cases, assuming all iodine is released immediately after sediment deposition (e.g., at the seafloor), or at great depth (e.g., 2 kmbsf). For example, when release is at the seafloor, the amount of released is such that the isotopic ratio 129I/127I is equal to the surface isotopic ratio 1500 × 10−15. On the other hand, iodine released at depth has been travelling with the sediments for some time (e.g., ts). In this case, the amount of initially released must be decreased due to decay, and such that the isotopic ratio 129I/127I corresponds to the sediment age ts at the point of release. We note that the actual value of MI initially released is unimportant because it is the isotopic ratio that determines the pore fluid age, rather than the individual concentrations. Additionally, we ignore any in situ production of 129I as a result of spontaneous 238U fission in the sediments. While this approximation may be appropriate for the sediments at Blake Ridge (see Fehn et al. ), it cannot be broadly applied to all locations due to variable natural uranium levels. At later times after release, (t) = (ts + tf) due to radioactive decay.
 A linear superposition of Equation ((15)) would be an exact solution of Equation ((9)) if the velocity was constant. An error is incurred in the linear superposition when the velocity field varies, but this error is small when the velocity variations occur over a length scale which is large compared with the diffusion distance (see Appendix A for details of the error estimate). In addition, the error due to the velocity variation is the same for both 127I and 129I, so the error in the ratio tends to cancel. Reliable pore fluid ages can be calculated using the ratio of concentrations, where each concentration is calculated by linear superposition.
 The resulting isotopic ratio is obtained by dividing the linear superposition of each iodine isotope composition as follows,
 Finally, the pore fluid age is obtained by solving for t in Equation ((1))
 Solving for the distribution of iodine using streamlines to quantify the advective transport is a computationally efficient alternative to a fully time-dependent model of coupled advective-diffusive transport, which would otherwise be necessary to account for the time dependence of 129I due to radioactive decay. This fully time-dependent model would need to be advanced in time over millions of years of sediment accumulation. Instead, we solve directly for a steady-state distribution of iodine by treating the diffusive transport separately. The small errors introduced by using this approximation (see Appendix) make this approach sufficiently accurate for the objectives of this paper. A schematic of our method is shown in Figure 1, and numerical parameters in Table 1.
 For one-dimensional sediment compaction, the sediment and fluid velocity are downward relative to the seafloor, as described by Equations ((3)) and ((4)). However, fluid expulsion causes upward flow relative to the sediment grains, so the net fluid velocity is slower than the sediments. This makes the pore fluid older than the host sediments. Additionally, the fluid velocity is proportional to ϕ(∞), the porosity at depth. Therefore, the smaller the value for ϕ(∞), the slower and older the fluid will be relative to the host sediments. Sediments that compact more completely create the largest age difference between the pore fluid and the host sediments.
 The sedimentation rate also determines the age of the pore fluid, although indirectly. This is because the fluid velocity is proportional to the sediment velocity, which in turn is proportional to . Faster sedimentation rates mean faster sediment and fluid velocities, which result in younger pore fluid ages. However, the relative age difference between the pore fluid and its host sediments remains determined by the completeness of compaction (e.g. ϕ(∞)).
 The pore fluid age, as measured at natural sites, is determined from the isotopic ratio of iodine, which is affected by both transport in the solid organic material and by subsequent transport in the pore fluid. While all pore fluid originates as seawater trapped between sediment grains at the seafloor, iodine may be released from organic matter into the pore fluid at any depth. If iodine is released into the pore fluid at the seafloor, then the age of the pore fluid and the age inferred from the iodine isotopes will be the same (neglecting the effects of in situ iodine production or diffusion). On the other hand, when iodine is transported below the seafloor in the organic material, the iodine age is equal to the sediment age. At the moment of release, the pore fluid will inherit this iodine, making it appear to have the age of the solid. However, due to preexisting iodine in the pore fluid, this signal becomes somewhat diluted. We account for this effect in the model, so the predictions can be compared with observations using different assumptions about the depth of iodine release. It is important to emphasize that we use ages based on iodine isotopes rather than the true pore fluid ages to constrain and test models of fluid flow in the subsurface.
 Figure 2A shows the results of our iodine transport model for one-dimensional sediment compaction when all iodine release occurs at the seafloor. The observations presented by Fehn et al.  are also shown for comparison (square data points with error bars). Sediment age appears as a dotted curve, and ranges between approximately 1–7 Ma in the depth interval shown (200–750 mbsf) for = 0.16 mm year−1. As expected, sediment age increases with depth. Additionally, the pore fluid age is shown as a range for several values of ϕ(∞), which represents the completeness of sediment compaction at great depth. The age range is bounded on the left (dashed line) given the iodine is transported by fluid advection only. The right bound (solid line) is given the iodine can additionally be transported by diffusion. In this case, allowing iodine diffusion produces older fluid ages, most likely because iodine from depth, being slightly older, can migrate back upward. However, we note that the solution between the pore fluid age with and without iodine diffusion considered differs by less than the largest error bar in the observations by Fehn et al. . Consequently, small errors in the model for effective diffusivity should not greatly influence the interpretation of our results.
Fehn et al.  argued that the pore fluid age at Blake Ridge, as predicted by a one-dimensional compaction model, should be significantly younger than the observations indicate. Our calculation supports this argument when sediment compaction is limited (i.e. ϕ(∞) = 0.43), and iodine diffusion is not considered. The dark bold dots in Figure 2A indicate the pore fluid age as presented by Fehn et al. , whose model is analogous to iodine transport by fluid advection only, with ϕ(∞) = 0.43, and = 0.1875 mm year−1. However, as compaction becomes more complete, the pore fluid age departs further from the age of the host sediments. When the value of ϕ(∞) < 0.15, pore fluid ages match those observed at Blake Ridge.
 Figure 2B shows the variation in pore fluid age for several values of , while keeping ϕ(∞) = 0.25. As compared to the sensitivity of the pore fluid age to ϕ(∞), variation between plausible sedimentation rates at Blake Ridge makes much less difference.
 Figure 2C shows the effect of iodine release location, R, on the pore fluid age for a one-dimensional compaction model when ϕ(∞) = 0.25 and = 0.16 mm year−1. The solid bold line gives the pore fluid age as a function of depth when all iodine release occurs at the seafloor. The pore fluid age increases with depth, as the iodine is carried deeper by the fluid. On the other hand, when iodine release occurs at depth, the surrounding local fluid will appear to adapt the age of the solid (when no diffusion is considered), which is considerably younger. This effect can be seen in the figure when the release depth is R = 400 and 600 mbsf, where a local minimum in the pore fluid age corresponds to the depth of release. In addition, above the release location, the pore fluid age decreases with depth, as iodine can only migrate upward (against the flow) by diffusion when the P é clet number is less than unity, where u and l are characteristic velocity and length scales. As release depth increases, the same pore fluid begins to appear very old. This is due to the great distance that iodine must travel back up to the shallow sediments by diffusion. Matching the pore fluid age with one-dimensional flow requires an iodine release depth of R ~ 2 kmbsf.
 Although our calculations predict that pore fluid ages can match the observations at Blake Ridge for a deep iodine release or nearly complete compaction, these results were obtained with a one-dimensional compaction model. As such, both sediment and fluid velocity are downward. Thus, iodine can only migrate upward by diffusion. In natural settings, fluid flow is likely more complex due to variations in the lithography, and not truly one-dimensional. To this end, we next explore the effect of anisotropic sediment permeability, seafloor topography, and fractures on the pore fluid age.
4.2 Age Due to Topography-driven Fluid Focusing
 Topographic features can cause focusing of pore fluids when the permeability permits preferential flow along sloped bedding layers. Even for small slopes (i.e. < 10°), focusing causes flow that is upward relative to the seafloor beneath the topographic feature. The larger the slope, the more effective the focusing becomes, causing an increased magnitude and spatial extent of upward fluid velocity [Frederick & Buffett, 2011].
 Focusing beneath topographic features can significantly change the fluid migration relative to a one-dimensional compaction model. Figure 3 shows the flow field in the top 1 km of the sediments when bedding layers are sloped 1.5°. Fluid pathlines, which originate throughout the sediments every 200 mbsf, illustrate the movement of pore fluids. The combination of lateral motion and reversals in direction can substantially increase the length of a fluid parcel's path relative to a one-dimensional compaction model. Focusing ultimately brings many pathlines toward the axis of topographic features.
 The contour plot in the background of Figure 3 shows the spatial distribution of pore fluid age within the sediments when all iodine release occurs at the seafloor. The complex spatial distribution is a result of iodine movement in the sediments along pathlines, or by diffusion. When topographic features cause pathlines to converge, pore fluid age tends to be oldest at the focal region, reflecting the fluid path. Moreover, the signature of iodine diffusion is two-fold. Diffusion can act to simply ‘smear’ or homogenize the fluid age over short distances, but in certain cases, it may be the only transport mechanism able to move iodine over long distances. For example, diffusion is the only mechanism that can bring deep iodine up to the shallow sediments in regions where both fluid and sediment velocity is downward.
 Figure 4A shows the pore fluid age as a function of depth at 0, 1, 2, and 4 km off the ridge axis for the same model parameters (e.g., θ = 1.5°, R = 0 mbsf). The pore fluid age is clearly the oldest at the ridge axis (i.e., at 0 km) which is the focal region and gets progressively younger toward the flanks. Because of the complex pattern of iodine transport, there is a large age variation between sites just a few kilometers apart. For example, the age difference between fluid at the ridge axis and that 4 km away varies by more than 20 Ma. Such large age differences predicted by our model suggest that measurements taken at only a single location may not be sufficient to characterize the fluid transport. Unfortunately, only one site at Blake Ridge has been measured for the iodine isotope ratio (e.g., site 997 by Fehn et al.  which was near the ridge axis). However, other large gas hydrate provinces, such as the Nankai Trough in Japan, do show substantial age variation between sites measured [Tomaru et al., 2007a]. Although the geological setting is different from the present study (Nankai Trough is an active margin), Tomaru et al. [2007a] report pore fluid ages which differ by ~ 10–20 Ma between the forearc basin and the outer ridge sites.
 When all iodine release occurs at the seafloor and is transported by fluid advection and diffusion, the pore fluid age at the ridge axis is roughly 10 Ma older than the age predicted by a one-dimensional compaction model for the same model parameters (e.g. θ = 1.5°; see comparison between Figure 4A and 2A). Decreasing the effects of diffusion by using n = 5 in Equation ((12)) increases the pore fluid age by ~ 5–10 Ma. Additionally, allowing more complete compaction by decreasing ϕ(∞) from 0.25 to 0.15 increases the pore fluid age in the shallow sediments by another ~ 10 Ma. The results of both these modifications are shown in Figure 4B. For topography-driven fluid focusing to produce fluid ages similar to the observations requires only small (but not unreasonable) changes in the lithographic parameters. Comparing Figure 4B with Figure 2A shows that the pore fluid age at the ridge axis (for n = 5 and ϕ(∞) = 0.15) is now more than twice as old as the age predicted by a one-dimensional compaction model for n = 3 and ϕ(∞) = 0.25. This represents an age difference of roughly +30 Ma.
 The pore fluid age, however, does not only depend on the distance a fluid parcel travels but also on its speed along the pathline. Therefore, it is possible for age to vary, even though the pathline length stays relatively constant. We have previously shown that increasing the strength of anisotropy in the sediment permeability (Kh/Kv), or increasing the angle of the bedding planes, can act to increase the effectiveness of fluid focusing within compacting marine sediments [Frederick & Buffett, 2011]. Figure 4A also shows the pore fluid age for several angles in the bedding planes. For a shallow source of iodine, the oldest pore fluid ages are predicted when the angle in the bedding planes is small. The two arrows in the figure indicate how the age at the ridge axis decreases when the angle in bedding is increased from 1.5° to 5° or 15°. While the overall pattern of flow remains similar over a range of slopes, larger slopes produce more effective focusing. This causes the velocity along pathlines to increase, and as a result, decreases the pore fluid age. In fact, focusing is so effective when θ > 5° that the majority (if not all) of the pore fluid in the domain is younger than what is predicted by a one-dimensional compaction model (see Figure 2 for comparison).
4.3 Age Due to Fracture-driven Fluid Focusing
 Fractured zones represent a region in the sediments where the vertical permeability is locally enhanced. Focusing and upward flow through these fractured zones depends on their permeability and spatial distribution. Figure 5 shows the pore fluid pathlines for a fractured zone of width W within the sediments. In this particular example, the fractured zone occupies 15% of the seafloor area. Details of flow do not depend on the dimensions of the fractured zone as long as the lateral position is defined relative to W. Pore fluid flows laterally as it is drawn toward the fractured zone. Once inside the fractured area, flow abruptly reverses direction, back toward the seafloor. We show a single (isolated) large fractured zone for easier visualization, but note that this general flow pattern scales for any fracture distribution.
 The contour plot in the background of Figure 5 shows the spatial distribution of pore fluid age within the sediments when all iodine release occurs at the seafloor. Pore fluid age is oldest within the fractured zone, as compared to fluid age within the surrounding matrix because of the long fluid pathlines that bring fluid back to the seafloor through the fractured zones. Unlike the flow patterns due to topography-driven focusing, fractures that extend to depth can tap old iodine, quickly bringing deep pressurized fluid and old iodine up to the shallow sediments. When the source of iodine is deep, fluid within the fractured zone appears younger than the surrounding matrix because deep iodine can quickly travel to the shallow sediments via advection through the fractures as compared to diffusion through the surrounding matrix.
 We have previously shown that fractured zones surrounded by anisotropic sediments are more effective at focusing pore fluids from the surroundings than those surrounded by sediments with isotropic permeability. In addition, increasing the strength of anisotropy of the fracture permeability (in this case, Kvf/Kv) or decreasing fracture density can act to increase the effectiveness of fluid focusing by draining a large volume of fluid through a smaller volume of fractured zones [Frederick & Buffett, 2011]. More effective focusing produces faster velocities within the fractured zone, leading to younger ages. For example, fluid within fractured zones with larger Kvf/Kv permeability ratios will appear younger due to increased velocity through the fractures. In terms of fracture density, the less of the seafloor that is fractured, the faster fluid must travel through the fractures to relieve overpressure. However, if the iodine particles must travel large distances before reaching an isolated fractured zone, the extra distance covered may actually increase the pore fluid age within the fractured zone.
 In natural settings, fractured zones are numerous and irregularly spaced throughout the sediments. When fractures are spaced closely enough, diffusion will act to homogenize the age difference between the fractures and surrounding matrix. Therefore, as fracture spacing is reduced, so is any apparent age difference between the pore fluid inside or outside of a fractured zone. Seismic reflection profiles of the Blake Ridge sediments detailed by Wood and Gettrust  show major fracture spacing at tens to hundreds of meters. Fractured zones placed at these intervals in our model (~ 200 m apart) are close enough that diffusion homogenizes the pore fluid age between the fractures and surrounding matrix. Only if the effects of diffusion are reduced or the fracture spacing is large will we expect an age difference between the matrix and the fractured zone (as shown in Figure 5).
 Figure 6 shows the pore fluid age as a result of several fractured zone densities within the sediments, for two iodine release depths (0 and 2 kmbsf). The spacing between fractures is held constant at 200 m, which allows diffusion to act between fractures, but fracture width is varied to obtain several possible densities. For example, a 20% density corresponds to fractured zone widths of 50 m with constant fractured zone spacings of 200 m. Although we varied the density of fractured zones widely, pore fluid age throughout the sediments tends to reflect the pore fluid age of the matrix. This is because the majority of the iodine is being transported through the matrix. When the iodine source is deep (dashed lines), the majority of the iodine is instead transported upward through the fractured zones. As a result, the pore fluid age is much older (due to the great distance the iodine must travel), and shows dependency on fractured zone density. For example, as fracture density decreases, the pore fluid age also decreases. This is a result of faster fluid advection when fracture density decreases. For densities 50% or higher, the pore fluid age returns to that of the one-dimensional compaction solution. The pore fluid age matches most closely with the observations at Blake Ridge when the source of iodine in fractured sediments is deep.
5 Discussion and Conclusion
 Our two-dimensional numerical model predicts the age of the pore fluid in compacting marine sediments based on iodine isotope ratios when natural features of the geometry at Blake Ridge are considered. Due to complexities in the lithology, such as anisotropic sediment permeability, topography, or fractures, fluid flow becomes focused with significant lateral motion or large looping pathlines. As a result, iodine transport and pore fluid age distribution become complex. A primary conclusion presented by Fehn et al.  to explain their observations was that methane and pore fluids migrated together to their current positions from depths between 1 and 3 kmbsf. While our results do show that fracture-driven fluid focusing can bring dissolved methane and pore fluid to the shallow sediments from those depths, the release depth of the iodine source required to match the observations (~ 2 kmbsf) is deep enough for thermogenic breakdown of organic material, assuming a geothermal gradient of 40 °C/km [Wood & Gettrust, 1998]. Iodine's strong association with the breakdown of organic matter plausibly connects it to the methane source in marine sediments. At Blake Ridge, there is no evidence that the hydrate contains predominantly thermogenic sources of methane. Rather, the biogenic nature of the methane source suggests that it originated at much shallower depths [Paull et al., 2000]. A shallow iodine release, on the other hand, produces ages that are too young when the sediments are fractured. This result is also supported by the numerical model presented by Lu et al. [2008b], which suggests that local release of young iodine (i.e., a shallow source) must be relatively minor in comparison to the contribution of migrating fluids which can carry large amounts of old iodine from deep sources.
 However, our calculations show that a deep source is not necessary for the pore fluid age to appear as old as the observations at Blake Ridge. Fluids focused beneath topographic features can produce pore fluid ages which match the observations fairly well by tapping shallow iodine- and methane-rich pore waters from an extensive source region extending several kilometers. Such focusing can transport iodine over great distances laterally, producing very old pore fluid ages at the ridge axis.
 Hydrate will form only when the methane concentration is in excess of the local solubility, which increases with depth. This condition is easiest to achieve when flow is locally upward relative to the seafloor, which is feasible in marine sediments with anisotropic permeability beneath regions of topography and through high-angle fractures due to pore fluid focusing. However, fluid focused by topography alone produces only weak upward fluid velocity which is limited in spatial extent when compaction is not complete. For example, the maximum upward fluid velocity at the seafloor for the model parameters used in Figure 4B is 0.007 mm year−1. Additionally, upward flow is spatially limited to the top 100 m beneath the topographic feature. In comparison, a minimum upward fluid velocity of 0.08 mm year−1 (at the seafloor) was required by Egeberg and Dickens  to match observed bromide and iodide profiles in the sediments in their numerical study. On the other hand, upward fluid velocity through high-angle fractured zones is sufficiently fast enough to match those required by previous modelling efforts [Frederick & Buffett, 2011].
 These results seem to suggest that the role of fractures and the fast upward flow they create is important for hydrate formation. However, the pore fluid age in fractured sediments does not match the observations at Blake Ridge unless the iodine source (and therefore the methane source) is deep. Perhaps, the fracture network at Blake Ridge is poorly connected and less effective than that assumed in our model, which would act to increase pore fluid age while still creating upward flow. Alternatively, a much lower value for the effective iodine diffusivity could increase the age, although the change required to explain the observations is unrealistic. The flow field as a result of topography-driven fluid focusing allows access to a laterally extensive methane source region for hydrate deposits beneath the ridge axis. This flowfield enhances methane transport toward the ridge axis, but pure lateral fluid movement should not result in any additional hydrate formation in the pore space due to the depth dependence of the methane solubility curve. Allowing for more complete sediment compaction can increase the spatial extent of the region with locally upward flow, while still producing pore fluid ages in line with the observations. Moreover, some combination of fractured zones and anisotropic sloped bedding planes no doubt exists within natural settings. Future studies should investigate the effect of combining the two end-member cases presented here and expand the model to include methane transport and the resulting hydrate distribution.
Appendix A: Error Analysis
 In order to calculate the pore fluid age according to ((19)), the time since iodine release must be assigned as a property of the unstable iodine isotope 129 I because of its time-dependent decay. A Lagrangian scheme is adapted so that this property can easily be tracked. While this method is beneficial for iodine advection, calculating the effects of iodine diffusion is not straight forward and requires some approximation. We assume the entire parcel of iodine initially released into the pore fluid at (x = xf, y = yf, tf = 0) is advected with the velocity of its center (), and that the composition at later times is determined by a linear superposition of ((15)). This is an exact solution to ((9)) if the velocity field is constant. However, because the velocity field varies spatially, the resulting iodine composition is only a good approximation to the exact solution when the length scale over which velocity varies spatially is large compared to the diffusion distance, or the iodine composition after superposition is nearly uniform. We use the solution to Equation ((9)), for constant u, to approximate the iodine mass distribution when the velocity field is quasi steady over the diffusion distance. We define the iodine mass distribution at each point along the pathline as a weighted average,
where the weights, wi(x,y,tf), are simply based on the bell shape of the diffusion solution, e.g.,
We use order of magnitude estimates to quantify the error in this approximation as follows.When tf becomes large, strain in the flow can cause the increasingly larger spread of iodine particles (with radius ) to become distorted. A measure of distortion can be estimated by comparing the radius of the growing parcel to the characteristic length scale of the variations in the velocity field, , which is obtained from
Here, the numerator is the local magnitude of velocity and the denominator is the local second invariant of the strain rate. For a single parcel of iodine, the error due to parcel distortion is small when the ratio . However, the solution for iodine composition is a superposition of the mass distribution based on the concentration at each point along every pathline. Parcel distortion will not contribute any error to the solution of iodine mass distribution if the concentration of iodine is uniform throughout the domain, which may be the case after superposition. Therefore, the ratio alone clearly does not capture the whole story.When particle distribution is nearly homogeneous, the net diffusive flux, J = De ∇ C, is essentially zero. A characteristic length scale for variation in the mass distribution can be estimated by
where the denominator is the magnitude of the local gradient of the mass distribution. For an isolated parcel, we expect to equal r. However, the length scale cannot be estimated by as it can for a single spreading iodine parcel because the parcels which make up the local superposed concentration field may each have different values of tf, for example. is large when the iodine concentration field approaches homogeneity. Therefore, when the ratio , it means the resulting iodine composition is homogeneous over the extent of the individual iodine parcels.An iodine mass distribution which is nearly homogeneous reduces the error associated with iodine parcel distortion due to strain in the flow field. Therefore, we estimate that the total error due to our assumption that the entire parcel of iodine travels with the velocity of its center is acceptably small as long as the ratio remains less than unity. This is the case when either or is large compared to r. We have ensured that is everywhere less than unity for all results presented. For flow in sediments with sloped bedding planes, a typical value in the 200–700 mbsf depth range near the ridge axis is ~ 0.30.
 This work is partially supported by funding from the Department of Energy (DE-PS26-08NT43260-0). We wish to thank the reviewers for their thoughtful feedback and thorough review of this paper.